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hal-00598569, version 1

Affine cones over Fano threefolds and additive group actions

Takashi Kishimoto () 1, Yuri Prokhorov () 2, Mikhail Zaidenberg () 3

(2011-06-06)

Abstract: We address the following question: When an affine cone over a smooth Fano threefold admits an effective action of the additive group? In this paper we deal with Fano threefolds of index 1 and Picard number 1. Our approach is based on a geometric criterion from our previous paper, which relates the existence of an additive group action on the cone over a smooth projective variety X with the existence of an open polar cylinder in X. Non-trivial families of Fano threefolds carrying a cylinder were found in loc.cit. Here we provide new such examples.

  • 1:  Department of Mathematics, Faculty of Science, Saitama University
  • Saitama University
  • 2:  Department of Algebra, Faculty of Mathematics, Moscow State University
  • Moscow State University
  • 3:  Institut Fourier (IF)
  • CNRS : UMR5582 – Université Joseph Fourier - Grenoble I
  • Domain : Mathematics/Algebraic Geometry
  • Keywords : Affine cone – Fano variety – Automorphism – Additive group – Group action
  • Internal note : IF_PREPUB
  • Comment : 20p.
 
  • hal-00598569, version 1
  • http://hal.archives-ouvertes.fr/hal-00598569
  • oai:hal.archives-ouvertes.fr:hal-00598569
  • From: Mikhail Zaidenberg <>
  • Submitted on: Monday, 6 June 2011 21:11:47
  • Updated on: Tuesday, 7 June 2011 09:15:03